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May 25, 20260 citationsOpen Access

Interface-Led Architecture and the Riemann Hypothesis: A System-Governance Heuristic for Prime Distribution and Dynamic Equilibrium

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TSTakuya Sogawa

Key Points

  • The paper seeks to present a heuristic interpretation of the Riemann Hypothesis through Interface-Led Architecture.
  • Maps primes to oscillatory Providers and zeta zeros to cancellation contracts.
  • Introduces a finite prime-mode energy model with defined roles including Provider, Observer, Operator, and Contract.
  • Reviews notes to clarify circularity warnings and strengthens the non-proof boundary involving prime oscillations.
  • Introduces organizational vocabulary that connects prime oscillations with analytic constraints.
  • Strengthens understanding of the Riemann Hypothesis concepts without providing a proof.
  • Offers a bridge to Riemann's explicit formula for the Chebyshev function and clarifies potential misleading expressions.

Abstract

This technical note presents a conceptual and heuristic system-governance interpretation of the Riemann Hypothesis through Interface-Led Architecture (ILA). It does not claim to prove the Riemann Hypothesis. The paper maps primes to oscillatory Providers, zeta zeros to cancellation contracts, and the critical line to a governance boundary between divergent and over-damped prime-mode phases. It introduces a finite prime-mode energy model and uses the vocabulary of Provider, Observer, Operator, Contract, and Governance Boundary to organize the relationship between prime-side oscillations and analytic cancellation constraints. This reviewed edition strengthens the non-proof boundary by adding heuristic notes to major sections, explicit circularity warnings around RH-equivalent error estimates, a more concrete bridge to Riemann's explicit formula for the Chebyshev function, and an appendix of potentially misleading expressions and safer replacements. It also notes that implementation references, GitHub links, commit hashes, and function-to-interface mapping tables are deferred to a future version. The English manuscript is the canonical version. The Japanese manuscript is included as a companion translation.

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Cite This Study

Takuya Sogawa (2026) studied this question.

synapsesocial.com/papers/6a13e8520e02ee3982d33154https://doi.org/10.5281/zenodo.20351129
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